Wave-induced Mean Currents Flowing Through Submerged Vegetation

A theory is developed for forcing of mean currents as waves propagate through canopies of submerged vegetation. Water particles experience variations in frictional drag as they are displaced through a variable-density canopy. When averaged over a wave period, the resulting mean drag on a water particle generates a mean current, consistent with previous models. The Lagrangian-mean drag is shown to equal the convergence of the wave-induced momentum flux. Where vegetation density increases with depth, momentum fluxes force Eulerian mean currents in the wave propagation direction, with magnitude proportional to, but sometimes larger than, the Stokes drift. Forcing reverses if vegetation density decreases with depth. These results for rigid vegetation are contrasted with the case of flexible vegetation, using established theories to predict small-tilt vegetation motions. Sufficiently far above the bed, given highly flexible stems, wave-frequency stem and water motions are almost equal. In this case, stems experience, and exert a drag on, the Lagrangian mean velocity. Consequently, sufficiently far above the bed, waves propagating through highly flexible vegetation force an Eulerian mean flow that cancels the Stokes drift, and stems develop a mean tilt in the propagation direction. In contrast, nearer the bed waves force an Eulerian mean velocity in the propagation direction. For typical natural canopies, in which vegetation density increases with depth, theory predicts a continuous transition, from Eulerian mean flows in the wave propagation direction for nearly rigid stems, to oppositely-directed flows canceling the Stokes drift far above the bed as stems become very flexible.